That is, if you lose with a rock, you have lost to a paper, hence a paper might start looking like a better option.
I guess, taken all over the world, most permutations show up.
This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself.
Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate.
This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on.
As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.
The advice in the article - bias towards previous opponent win is just an under-specification of how to play a no regret strategy (alter your distribution to match opponent play, which is more or less what your example describes). If you've already installed a random number generator in your brain then playing optimally (in the sense that it will exploit weakness and shift to random as necessary) can be very easily done via a no-regret algorithm such as randomized weighted majority.
This class of algorithm is proven to converge on the NE for zero-sum games while being much quicker than linear programming (this actually has practical consequences for poker bots - see counterfactual regret).
You can still use game theory to analyze the game though, if you "include" the player model into the game model.
"Rock-paper-fool goes like this. First a coin if flipped without you seeing If tails, you face a fool npc, who will play according to..., if head, you face a (homo economicus) player"
You could then try to analyze the equilibria of this game.
Pardon my ignorance of poker, but won't the opponent notice that you have suddenly raised the stake and that something could be afoot?
So - you play for 4-5 hours, folding on weak hands, and always raising on strong hands, and then, once people think you are a grinder, you start betting on weak hands; other players fold because they were used to you betting high stakes only on strong hands, you take their money.
In my opinion, the parent example was rather oversimplified. If a player started playing more aggressively, that would be an obvious 'tell'. Most opponents would recognise that they should play more conservatively until they figure out what's going on.
However, this strategy really just needs one sucker: if it works, it works.
I thought the chance of winning with no prior is 1/2... Otherwise, okay, you win with 1/3, your opponent wins with 1/3, and where is the other 1/3? :) I know what the article means, but they phrase is wrongly.
Wouldn't that remaining 1/3 be the odds for it being a draw?
If you replay when a draw occurs, then of course you have a 1/2 chance of winning.
To exploit that, the best strategy would probably be to always pick the move that wasn't played. Should give you an edge until your opponent notices your pattern :)
Since humans are bad at random, "just play randomly" doesn't really work; humans don't have access to "random" to play that way. So you often do get into the sorts of strategies you mention, to compensate for this.
Besides, it's more fun this way.
I believe there's a natural intuition for reading the expected movements of the other player, and have seen this reproduced (if anecdotally by only testing between myself and her, and not recording results) hundreds of times. Like you, 10-12 streaks of ties were not uncommon, certainly less common than statistics would seem to dictate.
somewhat relevant, there's a competitive league: http://www.usarps.com/
I always wanted to see it in vegas: https://www.youtube.com/watch?v=htX4T20t6lU
EDIT: clarity
I've tried coding it up here:
https://gist.github.com/andyhmltn/5c8c5734fe894db5aa02
Baring in mind it was a rushed 5 minute bodge-job so it could be wrong but there seems to be a massive skew towards draws
After more tests with this code it seems there's an 11% chance of winning if it's random. Baring in mind javascripts RNG
The only time to differ from true random is if you figured out your opponent's pattern.
Which can lead to some interesting strategy of making your opponent think he figured out your pattern. Then use your knowledge of what he thinks you will do to win.
It uses data gathered from other players. I remember playing it at the time and it was creepy how good it was at beating me. Oddly it didn't do so well this time. Maybe because I've just read that article.
If we assume most players play similarly, and don't remember much more than the last three results, this works really well.
> Humans are really bad at random
You could use the digits of some transcendental number, say, pi. Skip zeros, then each digit yields two moves. For the first move, lows(1,2,3) gives stone, mids(4,5,6) gives paper, and highs(7,8,9) gives scissors. For the second move use mod 3, so 0 gives stone, 1 gives paper, and 2 gives scissors.
